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        <h2 id="multicopter-design-and-control"><span>Multicopter Design and Control</span></h2>
        <p><span>The research on multicopter design and control has been summarized in book [1].</span></p>
        <h3 id="multicopter-design"><span>Multicopter Design</span></h3>
        <ul>
          <li><span>Based on Performance</span></li>
        </ul>
        <p><span>Multicopters are becoming increasingly important both in civil and military fields. Currently, most multicopter propulsion systems are designed by experience and trial-and-error experiments, which are costly and ineffective. We have proposed a comprehensive offline evaluation algorithm for multicopter performance in [2], an analytical design optimization method for electric propulsion systems in [3], efﬁciency optimization and component selection in [4]. Based on the previous work, design automation and optimization methodology for electric multicopter is proposed in [5]. With these work, a website </span><a href="http://www.flyeval.com" target="_blank" class="url">www.flyeval.com</a><span> has been launched by our group since 2016.</span></p>
        <ul>
          <li><span>Based on Controllability</span></li>
        </ul>
        <p><span>It has long been known that control performance is an important property of a plant. However, few works consider the control performance when selecting the appropriate propulsion systems for multicopters. If the considered multicopter is not sufficiently controllable, then the propulsion system needs to be redesigned according to specific control requirements, which are a waste of time and money. The studies focus on selecting the propulsion system in [6] and configuration in [7] for multicopters by taking the controllability into consideration.</span></p>
        <h3 id="multicopter-control"><span>Multicopter Control</span></h3>
        <p><span>Attitude control of a multicopter subject to uncertainties and disturbances is studied [8],[9],[10],[11],[12], where some failures under control are also taken as disturbances. However, some failures will cause multicopters out of controllability. It is pointed out that classical controllability theories of linear systems are not sufficient to test the controllability of multicopters. Study [13] makes controllability analysis based on the theory of positive controllability [14]. Degraded control is further proposed for a class of hexacopters subject to rotor failures [15].</span></p>
        <p><strong><span>Papers</span></strong></p>
        <p><span>[1] Quan Quan. Introduction to Multicopter Design and Control. Springer, Singapore, 2017.</span></p>
        <p><span>[2] Dongjie Shi, Xunhua Dai, Xiaowei Zhang, and Quan Quan. A practical performance evaluation method for electric multicopters. IEEE/ASME Transactions on Mechatronics. 2017, 22(3):13371348.</span></p>
        <p><span>[3] Xunhua Dai, Quan Quan, Jinrui Ren and Kai-Yuan Cai. An analytical design optimization method for electric propulsion systems of multicopter UAVs with desired hovering endurance. IEEE/ASME Transactions on Mechatronics, 2019, 24: 228-239.</span></p>
        <p><span>[4] Xunhua Dai, Quan Quan, Jinrui Ren and Kai-Yuan Cai. Efﬁciency optimization and component selection for propulsion systems of electric multicopters. IEEE Transactions on Industrial Electronics, 2019, 66(10): 7800–7809.</span></p>
        <p><span>[5] Xunhua Dai, Quan Quan, Kai-Yuan Cai. Design automation and optimization methodology for electric multicopter UAVs. Online: </span><a href="https://arxiv.org/abs/1908.06301" target="_blank" class="url">https://arxiv.org/abs/1908.06301</a></p>
        <p><span>[6] Guang-Xun Du and Quan Quan. Optimization of multicopter propulsion system based on degree of controllability. AIAA Journal of Aircraft, accepted, online: </span><a href="https://doi.org/10.2514/1.C035150" target="_blank" class="url">https://doi.org/10.2514/1.C035150</a></p>
        <p><span>[7] Binxian Yang, Guang-Xun Du, Quan Quan, Kai-Yuan Cai. The Degree of Controllability with Limited Input and an Application for Hexacopter Design. The 32nd Chinese control conference, Xi’an, 2013, 113-118. (in Chinese)</span></p>
        <p><span>[8] Ruifeng Zhang, Quan Quan, Kai-Yuan Cai. Attitude control of a quadrotor aircraft subject to a class of time-varying disturbances. IET Control Theory &amp; Applications, 2011, 5(9): 1140-1146.</span></p>
        <p><span>[9] Quan Quan, Guang-Xun Du, Kai-Yuan Cai. Proportional-integral stabilizing control of a class of mimo systems subject to nonparametric uncertainties by additive-state-decomposition dynamic inversion design. IEEE/ASME Transactions on Mechatronics. 2016, 21(2):1092 – 1101.</span></p>
        <p><span>[10] Bai-Hui Du, Andrey Polyakov, Gang Zheng and Quan Quan. Quadrotor trajectory tracking by using fixed-time differentiator. International Journal of Control, 2019, 92(12): 2854–2868.</span></p>
        <p><span>[11] Guang-Xun Du, Quan Quan, Kai-Yuan Cai. Additive-state-decomposition-based dynamic inversion stabilized control of a hexacopter subject to unknown propeller damages. The 32nd Chinese control conference, Xi’an, 2013, 6231-6236.</span></p>
        <p><span>[12] Jing Zhang, Guang-Xun Du, Quan Quan. Initial research on vibration reduction for quadcopter attitude control: an additive-state-decomposition-based dynamic inversion method. 2017 Chinese Automation Congress (CAC), Oct. 20-22, 2017, Jinan, China.</span></p>
        <p><span>[13] Guang-Xun Du, Quan Quan, Binxian Yang and Kai-Yuan Cai. Controllability analysis for multirotor helicopter rotor degradation and failure. Journal of Guidance, Control, and Dynamics, 2015, 38(5): 978-985.doi: 10.2514/1.G000731</span></p>
        <p><span>[14]Guang-Xun Du, Quan Quan. Degree of Controllability and Its Application in Aircraft Flight Control. Journal of System Science and Mathematical Science, 2014 Vol. 34 (12): 1578-1594. (in Chinese)</span></p>
        <p><span>[15] Guang-Xun Du, Quan Quan, Kai-Yuan Cai. Controllability analysis and degraded control for a class of hexacopters subject to rotor failures. Journal of Intelligent &amp; Robotic Systems, 2015, 78(1): 143-157.</span></p>
        <h2 id="probe-and-drogue-autonomous-aerial-refueling"><span>Probe and Drogue Autonomous Aerial Refueling</span></h2>
        <p><span>Probe-and-drogue refueling is widely adopted owing to its simple requirement of equipment and flexibility, but it has an apparent drawback that the drogue position is susceptible to disturbances. There are three types of disturbances: atmospheric turbulence, trailing vortex of the tanker, and bow wave effect caused by the receiver. The former two disturbances are independent of the receiver, whereas the bow wave effect, which depends on the state of the receiver, greatly influences the docking within a close distance [1].</span></p>
        <p><span>To deal with this problem, we start the study from modeling, especially the bow wave effect on docking control [2],[3]. On the whole, there still exist some challenges to designing a docking controller for probe-and drogue refueling. First, the probe-and-drogue refueling system is complicated. Moreover, as one of the main disturbances in the docking stage, the bow wave effect is a repetitive nonlinear disturbance and highly related to the states of the receiver and the drogue, which also makes docking control difficult. Second, the problem of the “slow dynamics” to track the “fast dynamics” becomes together if the bow wave effect is taken into account. Some feedback control methods may result in a chasing process between the receiver and the drogue, which may cause over control. Besides, the chasing action may lead to impact and damage to the drogue and the probe, which is very dangerous and needs to be avoided according to ATP-56(B) issued by NATO (North Atlantic Treaty Organization). Third, influenced by the environment, some unexpected sensor delay may happen. We studied vision-based robust position estimation [4].</span></p>
        <p><span>Based on the model obtained, iterative learning control is applied to make docking control reliable [5], [6], [7]. Here,“reliability”means a small docking error, certain robustness against disturbances and uncertainties, and little dependence on the system model and sensors.</span></p>
        <p><span>Autonomous aerial refueling is vulnerable to various failures and involves co-operation among autonomous receivers, tankers and remote pilots. Dangerous flight maneuvers may be executed when unexpected failures or command conflicts happen. To solve this problem, a failsafe mechanism based on state tree structure is proposed [8]. The failsafe mechanism is a control logic that guides what subsequent actions the autonomous receiver should take, by observing real-time information of internal low-level subsystems such as guidance and drogue &amp; probe and external instructions from tankers and pilots.</span></p>
        <p><strong><span>Papers</span></strong></p>
        <p><span>[1] Quan Quan, Zi-Bo Wei, Jun Gao, Ruifeng Zhang, Kai-Yuan Cai. A survey on modeling and control problems for probe and drogue autonomous aerial refueling at docking stage. Acta Aeronautica ET Astronautica Sinica, 2014, 35(9): 2390-2410. (in Chinese)</span></p>
        <p><span>[2] Zi-Bo Wei, Xunhua Dai, Quan Quan, Kai-Yuan Cai. Drogue dynamic model under bow wave effect in probe and drogue aerial refueling. IEEE Transactions on Aerospace and Electronic Systems, 2016, 52(4): 1728-1742.</span></p>
        <p><span>[3] Xunhua Dai, Zi-Bo Wei, Quan Quan. Modeling and simulation of bow wave effect in probe and drogue aerial refueling. Chinese Journal of Aeronautics, 2016, 29(2): 448-461.</span></p>
        <p><span>[4] Yan Gao, Xunhua Dai, Quan Quan. Vision-based robust position estimation in probe-and-drogue autonomous aerial refueling. IEEE/CSAA Guidance, Navigation and Control Conference, Xiamen, 2018.</span></p>
        <p><span>[5] Xunhua Dai, Quan Quan, Jinrui Ren, Zhiyu Xi and Kai-Yuan Cai. Terminal iterative learning control for autonomous aerial refueling under aerodynamic disturbances. AIAA Journal of Guidance, Control, and Dynamics, 2018, 41(7):1576-1583.</span></p>
        <p><span>[6] Xunhua Dai, Quan Quan, Jinrui Ren, Kai-Yuan Cai. Iterative learning control and initial value estimation for probe–drogue autonomous aerial refueling of UAVs. Aerospace Science and Technology, 2018, 82: 583-593.</span></p>
        <p><span>[7] Jinrui Ren, Xunhua Dai, Quan Quan, Zi-Bo Wei and Kai-Yuan Cai. Reliable docking control scheme for probe–drogue refueling. AIAA Journal of Guidance, Control, and Dynamics, accepted, DOI: 10.2514/1.G003708</span></p>
        <p><span>[8] Ke Dong, Quan Quan and W. Murray Wonham. Failsafe mechanism design for autonomous aerial refueling using state tree structures. Unmanned Systems, 2019, 07(04): 261–279. Code: </span><a href="https://github.com/KevinDong0810/Failsafe-Design-for-AAR-using-STS" target="_blank" class="url">https://github.com/KevinDong0810/Failsafe-Design-for-AAR-using-STS</a></p>
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